Bootstrapping SCFTs with four supercharges

By Nikolay Bobev, S. El-Showk, D. Mazáč, M. Paulos. 2015

158 citations recorded by the source corpus.

A bstractWe study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension 2 ≤ d ≤ 4. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of d and use this to construct the superconformal blocks for any d ≤ 4. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the d = 2, N=2,2$$ \mathcal{N}=\left(2,\;2\right) $$ minimal model with central charge c = 1 and the theory of a free chiral multiplet in d = 4, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/84133c01dc4d57e20f670a2e4643ece4c52b221b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Carving out OPE space and precise O(2) model critical exponents (2019, background): “See for instance [43–51] or [52–74] for supersymmetric studies.”
Bootstrapping 3D fermions (2015, result): “By numerically studying the fermionic crossing-equations in different dimensions, one could compare the evolution of the discontinuities to the results from a perturbative -expansion (similar to [57, 65]).”
Bootstrapping the O(N) archipelago (2015, unknown): “In recent years great progress has been made in the conformal bootstrap in d > 2, including rigorous bounds on operator dimensions and operator product expansion (OPE) coefficients [3–32], analytical constraints [33–45], and methods for approximate direct solutions to the bootstrap [46–49], includin”
A proof of the conformal collider bounds (2016, unknown): “[2–5, 61–72]).”
On the CFT operator spectrum at large global charge (2015, result): “J H E P 1 2 ( 2 0 1 5 ) 0 7 1 O(2) model, specifically [13], as well as for the W = Φ3 theory [31, 32], and it would be desirable to see how such analytic bootstrap methods may confirm and/or complement the results obtained in the present paper.”